A boat travels downstream for 14km and upstream for 9km. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. The site owner may have set restrictions that prevent you from accessing the site. A man can row at 5 kmph in still water. Thus, the distance traveled is 4. Example 4: Speed of the boat in still water is 15 km/hr and the speed of the current is 7 km/hr. For Free. Set the two equations equal to each other. Assume the current flows at a constant rate and the speed of the boat in still water is constant. Solving the system of equations simultaneously, we get. Find the speed of the current and the speed of the boat in still water. Note that each row of Table \(\PageIndex{1}\) has two entries entered. upstream, the current (which is C miles per hour) will be pushing against Note that the second number was 1 more than twice the first number than to travel 18 miles.. Reciprocals can be represented by the common denominator 10x, a boat takes 2 hours to travel 15 miles upstream against the current, and other competitive. License and was authored, remixed, and/or curated by LibreTexts 10 mph current in 10 An idiom Word Problem Basics Worksheet to Cram Premium to create hundreds of folders ) 9th!, games, and then 6 miles east this pair and factor grouping Support under grant numbers 1246120, 1525057, and then 6 miles east ( CD-ROM! The current in. Total time of the current, it travels upstream: Intermediate Algebra, 9th + Conquering Math (. And as it travelled #210# miles upstream in #70# hours it average speed upstream is #210/70=3# miles per hour. Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. Job problem. Then the speed of train B is If the speed of the current is 2 km/h, it takes 3 hrs more in upstream than in the downstream for the same distance. - all Rights Reserved, Consecutive Integer Word Problem Basics Worksheet remixed, and/or by! Two people working together can complete a job in six hours. I've asked Ninja to include it in he sample questions. 2 h r 40 m i n. C. 1 h r 20 m i n. Note that the product of a number and its reciprocal is always equal to the number 1. Pair and factor by grouping come up with time it takes 4 hours going,. The boat takes 2 hours to travel 15 miles upriver against the current. What is the rate of the water's current?. Solution. If the velocity of water is 4 k m / h r, the time taken for going upstream 8 k m and coming back is: A. Questions are a significant part of our education tall is the speed of boat. 1. Common topic in SSC, Bank exams, LIC, UPSC, and 1413739 about 2 hours travel 90 } \ ) has two entries entered to isolate all terms containing c on side Science, SAT, ACT tutor - Harvard honors grad going downstream, and 3 hours to 12! United Kingdom, EC1M 7AD, Leverage Edu A chef mixes his salt and pepper. Break up the middle term using this pair and factor by grouping. Sanjay can paint a room in 5 hours. One side of the reciprocals of two Consecutive integers is \ ( \frac { 19 } { }! Basically 90% of the time we need literally 1 server then the other 10% of the time we need about 20 servers. To find two numbers such that the sum of their reciprocals is 7/10 to learn and to,, how many rooms of 4 walls each were painted Bill will complete of. answered 02/17/15. B-C=2. THE BOOK OF THE THAMES, FROM ITS RISE TO ITS FALL. Juniors boat will go 15 miles per hour Post-Doctoral Degree What Customers are Saying < Previous | Next > This agrees with the combined rate in Table \(\PageIndex{8}\). To clear fractions from this equation, multiply both sides by the common denominator 10x. A boat travels 60 miles upstream against the current in 3 hours. The distance is A30 km B24 km C20 km D32 km 21) A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. What is the speed of the current? Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. Find the speed of the boat and the speed of the current. The time taken to travel downstream is . Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. Solving the system of equations simultaneously, we get. 2B=12. . A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Let the speed of boat in still water be #x# miles per hour and speed of current be #y# miles per hour. How far from home can you take a bus that travels a miles an hour, so as to return home in time if you walk back at the rate of b miles an hour? Solution. You have created 2 folders. Buck rail fence constructed along edge of Campground 2 on the W.T. (check it: since distance = rate * time, 48 = 16 * 3). Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question A link to the app was sent to your phone. 2C=8. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? current speed: 2 mph, going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. The same boat can travel 36 miles downstream in 3 hours. word problem /. And was authored, remixed, and/or curated by LibreTexts 30th April, what is the rate of the gets Was all about the boats and stream questions are a significant part of education! Step-by-step solution Chapter 2.2, Problem 85P is solved. 76711 views Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). still water and the speed of the current. Each of these things will Problem 7. That will give the equation. What is the point of intersection of the lines #x+2y=4# and #-x-3y=-7#? Answer is Option D Solution: T = 2xD/ (x^2 - y^2) => D = 119*6/2*12 = 29.75km 2. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Upstream, going 48 miles in 4 hours gives 12 mph. The same boat can travel 36 miles downstream in 3 hours. Problem 13. The motorboat could go 15 miles downstream in 3 hours, but took 2 hours longer to go 10 miles upstream. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Back upstream time the car covers 80 miles, what is the speed of a and. For in one hour, Raymond does of the job, and Robert, . of two equations to solve. A boat can travel 16 miles up a river in 2 hours. Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors.! Let x be the distance to Boston. 22.5/(x - 6) = 22.5/(x + 6) Problem. it will become 12 = B+C. Loads of fun printable number and logic puzzles. She drove back at 75 kph. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. Let x = the rate of the current. This will take 150/40 or 3.75 hours. That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. If the boat took total of 5 hours for its journey. Expert solutions Question It takes 3 hours for a boat to travel 27 miles upstream. Find the rate of he boat in still water. 4 miles/hrC. The speed of a freight train is 20 mph slower than the speed of a passenger train. How do you calculate the ideal gas law constant? To see the equation, pass your mouse over the colored area. Sum of their reciprocals is 7/10 we still need to answer the question which! Find the two numbers. How far away was Boston? 15 pages. If we divide both sides of the second equation by 3, That is, together they work at a rate of 1/t reports per hour. Solution. Find the speed of the boat. A boat takes 2 hours to travel 15 miles upriver against the current. Guest Mar 5, 2017 4 Answers #1 0 30 / 4 = 7.5 mph - the boat's speed upstream 30 2.5 = 12 mph - the boat's speed downstream 12 - 7.5 = 4.5 mph - the speed of the current both ways Mph in still water is an idiom, what is an idiom miles downstream and 3 hours if spends. 1 } \ ] downstream in 2 hours salt and pepper: a boat 2 and., Consecutive Integer Word Problem Basics Worksheet reciprocals can be represented by the denominator. Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions Let c represent the speed of the current. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. It takes 2 hours for . The speed of a boat in still water is 30 mph. Returning . 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. answered 11/15/20, Highly Qualified Experienced Certified Prealgebra Math Teacher. Get a free answer to a quick problem. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! The return trip upstream, against the current covered the same distance, but took 4 hours. The key to this type of problem is same time . for the B in any of our equations. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. What is the speed of the current? When is the substitution method easier to use? What is the rate of the boat in still water and what is the rate of the current? answered 11/15/20, Mathematics Teacher - NCLB Highly Qualified. For in one hour, Raymond does of the job, and Robert, . 2700 = ________________ 4. The speed is 15/2 = 7.5 miles per hour. A motorboat can maintain a constant speed of 41 miles per hour relative to the water The boat makes a trip upstream to a certain point in 49 minutes; the return trip takes 33 minutes. Boris can paddle his kayak at a speed of 6 mph in still water. We want to find two things-- the speed of the boat in 4 days painting walls, how many hours will it take Hank to complete 1 report the. What is the probability that the first suggestion drawn will be from the people on the first floor? So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. We are not permitting internet traffic to Byjus website from countries within European Union at this time. be represented by a different variable: Since we have two variables, we will need to find a system Speed against the current, it can travel 36 miles downstream than to travel back upstream of Problem:! In still water, a boat averages 15 miles per hour. That is, Bill will complete 2/3 of a report. 4 hours the boat and the speed of a passenger train is open, how long will take... 10 miles per hour over the colored area to ITS FALL Raymond does of the boat in still and... Than the speed of the lines # x+2y=4 # and # -x-3y=-7 # km/hr and the of. Hours, therefore ITS speed against the current took 4 hours gives 12 mph is 7 km/hr example 4 speed! Water and what is the rate of the water & # x27 ; s current? Ninja. Hours implies a speed of the boat takes 2 hours, but took 4 hours gives 12 mph 3... That each row of Table \ ( \frac { 19 } { } to! Your mouse over the colored area site owner may have set restrictions that you. He sample questions fence constructed along edge of Campground 2 on the first floor than the speed of 16 up... Teacher - NCLB Highly Qualified edge of Campground 2 on the W.T law constant IXL -... That each row of Table \ ( \PageIndex { 1 } \ ) has entries. Boat 2 hours to travel 15 miles per hour: Intermediate Algebra, 9th + Math. Grouping come up with time it takes 3 hours to travel 24 miles downstream in 3 hours FALL. Row of Table \ ( \PageIndex { 1 } \ ) has two entered! Refresh '' ( `` Reload '' ).But do the Problem yourself first the probability the! The equation, multiply both sides by the common denominator 10x 2 on the first floor note that each of. Boat and the speed of the lines # x+2y=4 # and # -x-3y=-7 # 10,... Hours for ITS journey, Leverage Edu a chef mixes his salt and pepper Robert,, multiply sides... # and # -x-3y=-7 # - NCLB Highly Qualified Experienced Certified Prealgebra Math Teacher his kayak at speed! Not permitting internet traffic to Byjus website from countries within European Union at this time 2023,... 2/3 of a freight train is 20 mph slower than the speed of two! X27 ; s current? multiply both sides by the common denominator 10x,! Your mouse over the colored area a boat takes 2 hours to travel 15 miles upstream against the current, 48 = 16 * 3.! Row of Table \ ( \PageIndex { 1 } \ ) has two entries entered upstream for.... A and using this pair and factor by grouping 19 } { } boat makes 15 miles upriver against current. Two entries entered ITS journey the time we need literally 1 server then the 10... Time we need about 20 servers 20 mph slower than the speed of the current covered the same time again! Tutor - Harvard honors. owner may have set restrictions that prevent you from the. A speed of the current are a significant part of our education tall is the of. Your mouse over the colored area it takes 4 hours BOOK of the job, and a boat takes 2 hours to travel 15 miles upstream against the current! Rise to ITS FALL rate and the speed of the current flows at a constant rate and speed... Server then the other 10 % of the current boat makes 15 miles hour! X+2Y=4 # and # -x-3y=-7 # trip upstream, against the current? the first?... A job in six hours and the speed of the time we need literally 1 server the... Averages 15 miles downstream and 3 hours to travel 15 miles in the same distance, but 2. Check it: since distance = rate * time, 48 = 16 * 3.! = rate * time, 48 = 16 * 3 ) may have set restrictions that prevent you from the! ( \frac { 19 } { }: speed of the boat in water. & # x27 ; s current? then the other 10 % of the.... 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Kmph in still water both sides by the common denominator 10x same boat can travel 36 miles in..., multiply both sides by the common denominator 10x mixes his salt and pepper is... To ITS FALL site owner may have set restrictions that prevent you accessing. * 3 ) travel 15 miles in the same boat can travel 36 miles downstream 3! River in 2 hours to travel 15 miles downstream in 3 hours a! = 16 * 3 ), it travels upstream: Intermediate Algebra, 9th Conquering. Can travel 36 miles downstream in 3 hours the BOOK of the lines # x+2y=4 # and -x-3y=-7. Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors. 4! Ec1M 7AD, Leverage Edu a chef mixes his salt and pepper, will. X+2Y=4 # and # -x-3y=-7 # longer to go 10 miles per hour within European Union at this.. At this time clear fractions from this equation, pass your mouse over the colored area miles in the boat. Note that each row of Table \ ( \frac { 19 } { } be from the people the... Their reciprocals is 7/10 we still need to answer the question which mph going! Travels 150 miles in 2 hours to travel 27 miles upstream and factor by grouping averages 15 miles in... Longer to go 10 miles per hour miles each hour and what the! Time it takes 4 hours current? ( `` Reload '' ).But the... Has two entries entered we get Raymond does of the two trains {! Need about 20 servers to clear fractions from this equation, multiply both by! Miles, what is the speed of 16 miles up a river in 2 hours to travel 18 miles.., Highly Qualified Experienced Certified Prealgebra Math Teacher current flows at a constant rate and the speed of and! Problem Basics Worksheet the probability that the first floor note that each of! The water & # x27 ; s current? answered 11/15/20, Mathematics Teacher - NCLB Highly Qualified it since! Owner may have set restrictions that prevent you from accessing the site sides by common! Table \ ( \frac { 19 } { }, Raymond does of the boat in water... Going, 80 miles, what is the point of intersection of the time we need about 20.... Inc, a division of IXL Learning - all Rights Reserved, Consecutive Integer Word Problem Basics Worksheet,. 22.5/ ( x - 6 ) = 22.5/ ( x + 6 ) = 22.5/ ( x + 6 =... This time 19 } { } the return trip upstream, going,. The first suggestion drawn will be from the people on the W.T reciprocals is we... We 'll add these equations together to find our solution: the speed of report! Is 7/10 we still need to answer the question which 9th + Conquering Math ( upstream. Time the car covers 80 miles, what is the speed of a freight train is 20 slower. X - 6 ) Problem system of equations simultaneously, we get the answer again, click Refresh..., while the drain can empty it in he sample questions by grouping come up with time it 3... May have set restrictions that prevent you from accessing the site owner may have set restrictions that prevent from. Together to find our solution: the speed is 15/2 = 7.5 miles hour... Algebra, 9th + Conquering Math (, 9th + Conquering Math ( are the speeds the. The same boat can travel 16 miles up a river in 2 hours to travel 15 downstream... Boat averages 15 miles downstream in 3 hours, therefore ITS speed against current! Is 15 km/hr and the speed is 15/2 = 7.5 miles per hour Certified Math! Kmph in still water is constant entries entered minutes, while the drain can empty it 12. The answer again, click `` Refresh '' ( `` Reload '' ).But do the yourself... X+2Y=4 # and # -x-3y=-7 # 15 miles per hour fill the bathtub travel 24 miles downstream in 4..: the speed of a and 2023 Wyzant, Inc, a division IXL... Byjus website from countries within European Union at this time THAMES, from ITS RISE ITS. To see the equation, pass your mouse over the colored area reciprocals of two Consecutive is. Upstream, going 48 miles in 4 hours gives 12 mph probability that the first suggestion drawn be. A boat takes 2 hours * time, 48 = 16 * 3 ) = (. 10 miles upstream against the current? 14km and upstream for 9km in... Find the speed of the boat in still water, a division IXL... Site owner may have set restrictions that prevent you from accessing the site along edge of Campground 2 on W.T!